Volume 41, Issue 1 (January 2013)
Fuzzy Testing for Regression Coefficient of Fuzzy Numbers
Statistical regression analysis is one of the important statistical methods and has been widely applied to different scientific areas. Classical regression analysis models are limited to crisp data. In practice, however, data are usually imprecise because data are difficult to measure precisely or data are determined subjectively. When dealing with fuzzy data, using classical regression analysis method to test the regression coefficient would be improper and lead to an incorrect decision. Regarding the topic of fuzzy regression analysis, most of the related literature focused on presenting methods of estimating regression coefficient in order to improve the ability of data interpreting. Unfortunately, those studies ignored the significance of the regression coefficient. That is, after constructing a fuzzy linear regression model, the regression coefficient must be tested as to whether they have the statistical meaning or not. The purpose of this paper is to develop a fuzzy testing method to test the regression coefficient with fuzzy data. Under the environment of crisp hypothesis, crisp critical value, and fuzzy data, the upper bound and lower bound of α-cuts of fuzzy testing statistics can be obtained based on α-cuts of fuzzy sets and extension principle. The membership function of fuzzy testing statistics can then be constructed. Finally, based on the membership function, a fuzzy testing method is developed to analyze those fuzzy data and further to make a statistical decision. Because the proposed testing method is based on membership function, when the data are crisp, the proposed approach can degenerate to the classical testing method.